1. PAT328, Section 3, March 2001 S7-1 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 SECTION 7 CHOICE OF ELEMENTS: TOPOLOGY AND RESTARTING

2. PAT328, Section 3, March 2001 S7-2 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 TABLE OF CONTENTS SectionPage 7.0 Choice of Elements: Topology and Restarting Geometric Overview……………………………………………………………………………………………………………..7-3 Element Topology…………………………………………………………………………………………………..7-4 Structural Element Types In MSC.Marc………………………………………………………………………….7-5 1d (Bar) Elements…………………………………………………………………………………………………..7-6 Beam Section Orientation Vector…………………………………………………………………………………7-7 2d Solid (Continuum) Elements…………………………………………………………………………………...7-8 2d Shell Elements (Thin Shell: 5 DOF @ Nodes)……………………………………………………………….7-10 2d Shell Elements (Thick Shell: 6 DOF @ Nodes)……………………………………………………………...7-11 3d Shell Elements (3 DOF @ Nodes)…………………………………………………………………………….7-12 1 st And 2 nd Order Elements………………………………………………………………………………………...7-13 Choice Of Elements………………………………………………………………………………………………...7-15 Connecting Elements Of Different Types………………………………………………………………………...7-17 Choice Of Integration Method……………………………………………………………………………………..7-18

3. PAT328, Section 3, March 2001 S7-3 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 OVERVIEW Selecting and Using Finite Elements  Element Topology Versus Element Property  Dimensions of Structural Space versus Dimensions of Finite Element  Connecting Elements of Different Topology Methods of Numerical Integration Plane Elements  Plane Strain  Plane Stress  Axisymmetry Orientation of Beam Cross Sections in Space Thin Shells Versus Thick Shells

4. PAT328, Section 3, March 2001 S7-4 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001  0-D Elements  1-D Elements Element Types in MSC.MARC  2-D Elements  3-D Elements ELEMENT TOPOLOGY

5. PAT328, Section 3, March 2001 S7-5 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 Example: First modal shape of beam model combining element types STRUCTURAL ELEMENT TYPES IN MSC.MARC 0-D Point Masses 1D (Bar) Elements 2D Solid (Continuum) Elements 2D Shell Elements 3D Solid (Continuum) Elements

6. PAT328, Section 3, March 2001 S7-6 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 1D (BAR) ELEMENTS Beam Elements (Standard, Euler- Bernoulli) Truss (Spar) Elements Axisymmetric Shell Elements Springs Dashpots (Use Springs Options  These elements may have nonlinear properties Example : Snap-through of Bottom of a Soft-Drink Can  Simulated with quadratic (3-node) 1D Axisymmetric elements  Aluminum can –plasticity included  When pressure increases the bottom of the can “snaps” thus increasing the volume inside the can –relieving the pressure- and preventing the rupture and spilling of contents.  Because of plasticity the bottom cannot return back to the original shape thus protecting the consumer from spoilage.

7. PAT328, Section 3, March 2001 S7-7 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 XZ Plane Node 1 Node 2 Y X Z 1” 2” J Izz Ixx Z Global CS X Y BEAM SECTION ORIENTATION VECTOR

8. PAT328, Section 3, March 2001 S7-8 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 Plane Stress Plane Strain 2D SOLID (CONTINUUM) ELEMENTS Plane Stress Elements (2 DOF @ nodes: Ux, Uy)  Planar structures, All out-of- plane stresses zero  Typical: Flat panels subject to inplane loads Plane Strain Elements (2 DOF @ nodes: Ux, Uy)  Planar model, All out-of-plane strains constant or zero  Typical: Slice of car’s door rubber seal Membrane Elements (3 DOF @ nodes: Ux, Uy, Uz)  Curved, very thin structures unable to sustain bending

9. PAT328, Section 3, March 2001 S7-9 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 Axisymmetric Elements (2 DOF @ nodes: Ux, Uy) Axisymmetric structures with axisymmetric loadings 2D SOLID (CONTINUUM) ELEMENTS (CONT.) X = Axial Y = Radial !

10. PAT328, Section 3, March 2001 S7-10 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 2D SHELL ELEMENTS (THIN SHELL: 5 DOF @ NODES) In-plane/out-of-plane loadings in planar and curved surfaces  Ignores out-of-plane normal stress  Ignores out-of-plane transverse shear stresses (Normals remain normals)  Thickness very small (<5%) compared to typical surface

11. PAT328, Section 3, March 2001 S7-11 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 2D SHELL ELEMENTS (THICK SHELL: 6 DOF @ NODES) In-plane/out-of-plane loadings in planar and curved surfaces  Ignores out-of-plane normal stress  Considers out-of-plane transverse shear stresses (Plane Sections remain Plane)  Thickness small (>5%, but <10%, ) compared to typical surface dimensions

12. PAT328, Section 3, March 2001 S7-12 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 3D SHELL ELEMENTS (3 DOF @ NODES) Considers all 6 components of stresses and strains Suitable for 3D solid bodies Although valid, 3D Solid Elements are neither efficient, nor very accurate for thin surfaces, or long and slender parts.

13. PAT328, Section 3, March 2001 S7-13 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 1 ST AND 2 ND ORDER ELEMENTS

14. PAT328, Section 3, March 2001 S7-14 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 1 ST AND 2 ND ORDER ELEMENTS (Cont.)

15. PAT328, Section 3, March 2001 S7-15 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 CHOICE OF ELEMENTS Use beam elements to model beam-like structures, if possible and appropriate.  They are economical and give very good answers within the assumptions of beam theory.  Also very useful to represent stiffeners on shells Example: Pantograph  Including beam-to- beam contact

16. PAT328, Section 3, March 2001 S7-16 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 CHOICE OF ELEMENTS (Cont.) For bending problems with solid elements (2D or 3D), element type and meshing can greatly affect the results.  Solid elements may be necessary in bending problems where beam theory is not sufficient if thickness is too large or stresses in the thickness direction are important.  How shall we choose the element type?  How fine a mesh do we need?

17. PAT328, Section 3, March 2001 S7-17 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 CONNECTING ELEMENTS OF DIFFERENT TYPES Part of the structure may be represented by shell elements and part by solid elements  The number of degrees of freedom is different for solid elements than for shell element  How to prevent the free rotation of the shell at the interface with the solid

18. PAT328, Section 3, March 2001 S7-18 MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001 CHOICE OF INTEGRATION METHOD Different methods of integration are available. Their performance is discussed in further detail in the next chapter  Standard Elements provide full integration  Materials with incompressible behavior (such as rubber) require special options such as Reduced Integration or Herrmann formulation. The reason for this is that a Poisson’s ratio of 0.5 will have an indeterminate stiffness coefficient Integration Points for Standard 8-Node Membrane Element